10-y-o dd looks at the multiple-step problem and figures it out in seconds, says the method in the book is way different from how she would do it, her way is way better, but she can't explain her way, just says the right answer was obvious to her and isn't it to everybody? Doesn't do this with every kind of math problem, but many different ones. Since then I've researched online for how to tell what it is she's doing, how to teach someone who thinks the way she does, what approach to use, and enrichment math for her, but I can't really find anything helpful.

Assuming she is arriving at the correct answers, I'm sure the methods she uses are out there somewhere. Everything in math has been done before by someone. You might try looking for books of math tricks. You might also try finding another math genius who can decypher what she is doing.

I watched an episode (Stan Lee's Superhumans) about one guy who had a odd brain condition where the parts of his brain normally used for spatial manipulation / movement (assuming I'm remembering correctly) were being used for math. For him math was sort of like navigating through a maze really, really fast. He could do things like multiply 20-digit numbers in his head in seconds, do long division to ridiculous numbers of decimal places, that sort of thing. Here's a snippet of the episode:
http://www.youtube.com/watch?v=dtotrboSUqQ_________________Homeschool Articles - Events - Support Groups

How could I go about finding a math genius to help us figure this out? I'd love to, but that's where I don't have a clue what to start with. Would a nearby university math dept be a useful resource at all?

I second the fact that elementary teachers as a rule do not have a math background. My wife is a high school math teacher. There is a similar example with us, I stopped by her Algebra 2 classroom years ago and she asked me how I would go about solving a question on the board and I just looked at it and gave her the correct answer but couldn't really explain how I got it. She is much better at following the rules and fomulas and sometimes I just "see" the answer.
Steven is probably a good person to contact, I could also get you in touch with my wife if you like. In any case it sounds like you have a bright daughter on your hands. As someone who also doesn't use the book way at arriving at solutions I would recommend that she still "learn" the book method, going forward she may need to show work for grades and you can reach a point that you need the book method to solve a problem.